Algebra, Topology and Related Fields, İzmir, Turkey, 22 - 23 September 2022, pp.2
A binary linear code C of length n is a subspace of the vector space F 2 n . The elements of C are
called codewords. For a non-zero codeword c in C, the support of c is the set of positions of
the coordinates of c which are non-zero. The Hamming weight of c, denoted by wt(c), is the
number of elements of support of c. The minimum weight of C, denoted by wt(C), is defined
as the minimum of Hamming weights of all non-zero codewords in C. A binary linear code is
called constant weight code if every non-zero codeword has the same Hamming weight. In
this talk we use the n-ary symmetric difference of the supports of the codewords in order to
give a construction for the binary linear constant weight codes. Moreover, we give a
characterization for the constant weight codes with given parameters in terms of supports of
the codewords. The arguments in this characterization lead us to construct binary linear
constant weight codes up to permutation equivalence. We also consider the permutation
automorphism group a constant weight code and prove that the order of the permutation
automorphism group of any given constant weight code of the dimension bigger than 2 is a
multiple of six.